The fused quinuclidine-valerolactone system Synthesis and conformation of 4-alkyl or 4-aryl-6-oxa-1-azatricyclo (4.2.2.027) dodecan-5-one

Michael addition of ethyl malonate, alkylmalonate and phenylacetate to 2-methylene-quinuclidin-3-one, followed by NaBH₄ reduction of the 3-oxo group in the resulting adduct, then acid hydrolysis and decarboxylation (in the case of malonates) gave 6-oxa-1-azatricyclo-(4.2.2.0^2,7)dodecan-5-one, its 4-alkyl and 4-aryl derivatives. A minor byproduct is 2-(trans-3-hydroxyquinuclidin-2-yl)-α-alkyl-propanoic acid which is unable to undergo cyclization to δ-lactone.     

LASER PHOTOLYSIS OF RETINAL AND ITS PROTONATED AND UNPROTONATED n-BUTYLAMINE SCHIFF BASE

Abstract —The pulsed ruby laser (347 nm) flash photolysis technique has been used to measure the triplet-triplet absorption spectra and triplet lifetimes of trans -retinal, N-frans -retinylidene- n -butylamine (NRBA), and protonated NRBA (NRBAH⁺) at room temperature. In methylcyclohexane solution, the triplet lifetimes are in the range 10–20 μs and decrease in the order NRBAH⁺ > NRBA > trans -retinal. Intersy stem-crossing efficiencies (φ_ISC) were determined by a comparison technique using anthracene and 1,2-benzanthracene as reference compounds. For trans -retinal, φ_ISC is 0–50 pM 0–05 in methylcyclohexane and 0–08 in methanol, which confirms that earlier values of 0–11 and 0–017 in these solvents are in error. For NRBA and NRBAH⁺ in methylcyclohexane, Φ_ISC values are 0008 and < 0–001, respectively. Evidence is presented for a significant solvent effect in the isomerization of retinal via the triplet state, and that cis φ trans isomerization occurs from the triplet state of NRBAH⁺. The relation between the intersystem-crossing properties of model compounds and the photochemistry of rhodopsin is discussed.     

Fractional colorings with large denominators

The m-chromatic number χ_m(G) of a graph G is the fewest colors needed so each node has m colors and no color appears on adjacent nodes. The fractional chromatic number is χ*(G)=lim_m→∞χ_m(G)/m. Let m(G) be the least m so that χ* (G) = χ_m(G)/m. For n node graphs, Chvátal, Garey and Johnson showed m(G) ≦ n^n/2 and gave example, where m(G) is asymptotically . This note gives examples where m(G) is asymptotically λⁿ, where λ ≈? 1.346193. © 1995 John Wiley & Sons, Inc.     

Hankel operators on planar domains

Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves LetA denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and letP denote the orthogonal projection ofL ²(Ω,dA) ontoA. A functionb inA induces a Hankel operator (densely defined) onA by the ruleH _b (g)=(I?P)bg. This paper continues earlier investigations of the authors and others by determining conditions under whichH _b is bounded, compact, or lies in the Schatten-von Neumann idealS _p , 1<p<∞     

The shapes of bowed interfaces in the two-dimensional Ising model

We show that properly normalized net energy fluctuations associated with interfaces in two-dimensional Ising models are described, asymptotically, by random walk partition functions. Two examples are investigated: one is a droplet on a wall, and the other is two nearby, ideally parallel interfaces; the mean shapes of the interfaces in both cases prove to be elliptic, bowed outward from the wall or from each other, the semiminor axis of the latter ellipse being 1/2 that of the former, in accord with random walk results.